Pries: 619 Complex Variables II. Projects. There are an enormous number of possible projects to choose from. Here are a couple topics from Miranda that would be interesting. I’d be happy to help you choose a topic which matches your interests. Quality is more important than quantity but you could aim for a 20 minute talk and an 8 page paper. Make sure to have an introduction, theory, examples, pictures/graphs as appropriate, and bibliography. 1. Miranda pg 67-70, 134-135, 143-145: Ramification divisors and Plucker’s formula. 2. Miranda pg 71-72, 98-102: Resolution of singularities and projections. 3. Miranda III.3: Group actions and bound on |Aut(X)| (Rodney?). 4. Miranda III.4: Monodromy (Galois theory). 5. Miranda V.4: Maps to projective space. 6. Proof of the Riemann-Roch theorem (other references might be easier). 7. Miranda VII.2: The canonical map and classification of curves. 8. Miranda pg 212-215 plus other references: Moduli spaces of curves of genus g. 9. Miranda VII.3: General position, Castelnuovo’s bound. 10. Miranda VII.4: Weierstrass points. 11. Modular curves (Number theory).